"tourists and business interests" describes two groups of people are complaining. Tourists are visitors from other countries who visit Times Square, which is a famous location in New York, and expect it to be a nice place to visit. "Business interests" mean the various business in Time Square who feel that the desnudas will drive away the kind of people they would like to have as customers. "Sign the bill into law" is part of the political process of lawmaking in the United States. I don't know the exact details which would vary from city to city, but, as with the national legislature, creating a law requires the approval of both the City Council and the Mayor, and the process is first that the "bill" is voted on by the city council, and then is approved by the mayor. The moment when the mayor puts his signature on the bill is the moment at which it becomes law, and is often treated as a ceremony and a photo opportunity for the news media.

"Desnuda" is Spanish for "naked." Newspaper accounts describe at some of the desnudas of Times Square as being from Venezuela, and as having Spanish surnames and speaking little English. "Desnuda" combines the ideas of being naked and Hispanic. Their body paint generally features themes such as American flags and "I Love New York." They are, in colloquial English parlance, not really "naked" or "nude," but "topless" or "half-naked." Their body paint gives the visual impression of a bikini top. "Seedy" is a perfectly good English word that means shabby or disreputable.

I believe ""desnudas" is Spanish and refers to naked women/females.